add
The addition of matrices satisfies the algorithm (A, B and C are all of the same type): it should be noted that addition can only be performed between matrices of the same type.
Digital multiplication
The addition, subtraction and multiplication of matrices are called linear operations of matrices.
exchange
The matrix produced by the row-column exchange of matrix A is called the transposed matrix of A, and this process is called the transposed matrix.
Extended data:
In physics, matrices have applications in circuit science, mechanics, optics and quantum physics. In computer science, three-dimensional animation also needs matrix. Matrix operation is an important problem in the field of numerical analysis.
Decomposition of a matrix into a combination of simple matrices can simplify the operation of the matrix in theory and practical application. For some widely used and special matrices, such as sparse matrix and quasi-diagonal matrix, there are concrete fast operation algorithms.
For the development and application of matrix related theory, please refer to matrix theory. Infinite-dimensional matrices will also appear in astrophysics, quantum mechanics and other fields, which is the generalization of matrices.
The main branch of numerical analysis is devoted to the development of effective algorithms for matrix calculation, which has been a topic for centuries and an expanding research field.
The matrix decomposition method simplifies the theoretical and practical calculation. The customized algorithm for specific matrix structures (such as sparse matrix and near-angle matrix) speeds up the operation speed in finite element method and other calculations. ?
Infinite matrix appears in planetary theory and atomic theory. A simple example of infinite matrix is the matrix representing the derivative operator of Taylor series of functions.
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